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There are several types of symmetry:

  • rotational symmetry: an object maps exactly onto another if rotated about an axis
  • translational symmetry: an object maps exactly onto another if moved along a line
  • reflective symmetry: an object maps exactly onto another if reflected along a line
  • and many combinations of the above, such as helical symmetry where an object maps exactly onto another if moved along a line and rotated about an axis.

· Rotoreflection symmetry

· Helical symmetry

· Non-isometric symmetries

· Scale symmetry and fractals

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Q: How many types of symmetry are there?
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